What does the storm that kill the Turks symbolise for the main characters?Hint: destructive love, ambition and concern for reputation.
The storm is a kind of pathetic fallacy that mirrors the jealous storm that will brew inside Othello once on Cyprus. There is much geographical symbolism in the play: Venice is represented by Iago, that which is white, Christian, civilized. Turkey is represented by Othello, that which is non-white, non-Christian, uncivilized. And Cyprus is represented by Desdemona; she is the island caught in the middle. She is the key to victory--whoever claims her, controls the Mediterranean, controls the island. Obviously, this is a sexist gender war. So, the storm is a symbol of Iago and Othello's battle to claim Desdemona. It is, as you mentioned, a symbol of destructive love, ambition, and reputation all by the males aimed at the females (Emilia and Bianca too, don't forget).
The storm is also a red herring; the Turks were such a worry to the Venetians in Act I. The Duke calls a special session of the Senate to discuss the war. In Act II, just as the battle begins, it ends--as if a God willed the Turks dead, a Deus ex Machina. So, Othello mistakenly thinks the war is over, but it is really just beginning. All of Venice in Act I was worried over the Turk (a representation of the dark side of Othello), and Othello thinks the Turk is no longer a threat. After his victory in court in Act I, Othello thinks of himself as part of the white, Christian, civilized world. He does not realize that Iago is exposing his darker half by preying on his jealous rage. Instead of fighting a conventional war with the Turks, Othello will fight a domestic war, and so the storm foreshadows the destruction to come. In the end, the storm (jealousy, hubris, sexism) destroys all.